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0-1-t-n-1-2-1-t-n-1-dt-

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Question Number 149944 by ArielVyny last updated on 08/Aug/21
∫_0 ^1 (t^((n−1)/2) /((1+t)^(n+1) ))dt
∫01tn−12(1+t)n+1dt
Commented by Ar Brandon last updated on 08/Aug/21
β(m, n)=∫_0 ^1 ((x^(m−1) +x^(n−1) )/((1+x)^(m+n) ))dx=∫_1 ^∞ ((x^(m−1) +x^(n−1) )/((1+x)^(m+n) ))dx
β(m,n)=∫01xm−1+xn−1(1+x)m+ndx=∫1∞xm−1+xn−1(1+x)m+ndx

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